From the previous section, it was clear the other existing rectangular LB schemes [1]}, [2]}, [3]}, [4]}, [5]} are limited to relatively low or moderate Reynolds number simulations due to numerical stability issues. This is generally due to their choice of orthogonal moment basis and construction of equilibria and the correction terms involving cumbersome specifications of several model parameters that limited the possible ranges of variation of their transport coefficients. These aspects have been avoided in the present work that uses a non-orthogonal moment basis, a matching principle to construct the equilibria directly from the Maxwell distribution function, and simpler expressions for tuning the transport coefficients and specifying the correction terms to restore isotropy. As a result, the RNR-LBM and RC-LBM developed here represent as significant improvements over the prior rectangular LB formulations. Now, between these two options, the simulations carried out earlier (see Table REF ) showed that the latter can deliver smaller global relative errors compared to the former in a body force driven flow. Besides such accuracy improvements, we will now clarify the utility of performing the collision step in the local moving frame of reference in the case of RC-LBM in improving the robustness of computations. In this regard, we will now perform two different types of numerical stability tests involving the shear flow generated within a square cavity due to the motion of the lid that compares the RNR-LBM and RC-LBM. Such systematic numerical stability investigations of rectangular LB formulations are lacking in the literature.
